DLMF:11.11.E10 (Q4771)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:11.11.E10
No description defined

    Statements

    DLMF defining formula
    𝐀 - Ξ½ ⁑ ( Ξ» ⁒ Ξ½ ) ∼ - 1 Ο€ ⁒ βˆ‘ k = 0 ∞ ( 2 ⁒ k ) ! ⁒ a k ⁒ ( - Ξ» ) Ξ½ 2 ⁒ k + 1 , asymptotic-expansion associated-Anger-Weber-A 𝜈 πœ† 𝜈 1 πœ‹ superscript subscript π‘˜ 0 2 π‘˜ subscript π‘Ž π‘˜ πœ† superscript 𝜈 2 π‘˜ 1 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim-\frac% {1}{\pi}\sum_{k=0}^{\infty}\frac{(2k)!\,a_{k}(-\lambda)}{\nu^{2k+1}},}}
    0 references
    constraint
    Ξ½ β†’ + ∞ β†’ 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
    0 references
    Symbols used
    Anger–Weber function
    DLMF defining formula
    𝐀 Ξ½ ⁑ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2abdec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    Ο€ {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1gdec
    0 references
    nonnegative integer
    DLMF defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1edec
    0 references
    parameter
    DLMF defining formula
    Ξ» πœ† {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S11.XMD3.m1bdec
    0 references
    expansion function
    DLMF defining formula
    a k ⁒ ( Ξ» ) subscript π‘Ž π‘˜ πœ† {\displaystyle{\displaystyle a_{k}(\lambda)}}
    xml-id
    C11.S11.XMD4.m1bdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q4771&oldid=24171863"
    Powered by MediaWiki